standing wave

Examples of standing wave in the following topics:

• Standing Waves and Resonance

  • A standing wave is one in which two waves superimpose to produce a wave that varies in amplitude but does not propagate.
  • The resultant looks like a wave standing in place and, thus, is called a standing wave.
  • Standing waves are found on the strings of musical instruments and are due to reflections of waves from the ends of the string. shows seven standing waves that can be created on a string that is fixed at both ends.
  • Standing waves in a string, the fundamental mode and the first six overtones.
  • A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).

• Standing Waves in Wind Instruments

  • But another great container for standing waves actually holds standing waves of air inside a long, narrow tube.
  • The standing waves in a wind instrument are a little different from a vibrating string.
  • The standing waves in the tubes are actually longitudinal sound waves.
  • Here the displacement standing waves in Figure 3.10 are shown instead as longitudinal air pressure waves.
  • See Standing Waves in Wind Instruments for more explanation.

• Standing Waves on a String

  • Standing wave occurs due to the interference when transverse waves in strings are reflected and the incident and reflected waves meet.
  • This vibration is just a very small standing wave.
  • A standing wave is a wave that appears stationary, meaning it remains in a constant position.
  • Standing waves appear to be standing still, hence the name. illustrates a very slow moving standing wave.
  • When we observe a standing wave on strings, it appears the wave is not moving but standing still.

• What is a Standing Wave?

  • They are tones caused by standing waves produced in or on the instrument.
  • Most sound waves, including the musical sounds that actually reach our ears, are not standing waves.
  • Instead, waves would seem to be appearing and disappearing regularly at exactly the same spots, so these trapped waves are called standing waves.
  • For any narrow "container" of a particular length, there are plenty of possible standing waves that don't fit.
  • But there are also many standing waves that do fit.

• Standing Waves on Strings

  • You may have noticed an interesting thing in the animation of standing waves: there are spots where the "water" goes up and down a great deal, and other spots where the "water level" doesn't seem to move at all.
  • All standing waves have places, called nodes, where there is no wave motion, and antinodes, where the wave is largest.
  • One "container" that works very well to produce standing waves is a thin, very taut string that is held tightly in place at both ends.
  • As a standing wave waves back and forth (from the red to the blue position), there are some spots called nodes that do not move at all; basically there is no change, no waving up-and-down (or back-and-forth), at these spots.
  • But any wavelength that doesn't have a node at each end of the string, can't make a standing wave on the string.

• Reflections

  • When these two waves have the same frequency, the product of this is called the standing waves.
  • Standing waves appear to be standing still, hence the name.
  • To understand how standing waves occur, we can analyze them further: When the incident wave and reflected wave first meet, both waves have an amplitude is zero.
  • When we observe standing waves on strings, it looks like the wave is not moving and standing still.
  • The points in a standing wave that appear to remain flat and do not move are called nodes.

• The Wave Function

  • The most common symbols for a wave function are ψ(x) or Ψ(x) (lowercase or uppercase psi, respectively), when the wave function is given as a function of position x.
  • The wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation.
  • This explains the name "wave function" and gives rise to wave-particle duality.
  • The trajectories C-F are examples of standing waves, or "stationary states. " Each standing-wave frequency is proportional to a possible energy level of the oscillator.
  • Relate the wave function with the probability density of finding a particle, commenting on the constraints the wave function must satisfy for this to make sense

• Longitudinal and Transverse Waves

  • Normally, these changes are travelling (except for standing waves); the disturbance is moving away from whatever created it, in a kind of domino effect.
  • Most kinds of waves are transverse waves.
  • Sound waves are longitudinal waves.
  • A mathematical description might be that in longitudinal waves, the waves (the disturbances) are along the same axis as the direction of motion of the wave; transverse waves are at right angles to the direction of motion of the wave.
  • In water waves and other transverse waves, the ups and downs are in a different direction from the forward movement of the wave.

• Energy Transportation

  • The force you feel from a wave hitting you at the beach is an example of work being done and, thus, energy being transfered by a wave in the direction of the wave's propagation.
  • Energy transportion is essential to waves.
  • It is a common misconception that waves move mass.
  • One easy example is to imagine that you are standing in the surf and you are hit by a significantly large wave, and once you are hit you are displaced (unless you hold firmly to your ground!).
  • Again, this is an easy phenomenon to experience empirically; just stand in front of a faster wave and feel the difference!

• Radio Waves

  • Radio waves are EM (Electromagnetic)waves that have wavelengths between 1 millimeter and 100 kilometers (or 300 GHz and 3 kHz in frequency).
  • Like all other electromagnetic waves, radio waves travel at the speed of light.
  • The abbreviation AM stands for amplitude modulation—the method for placing information on these waves.
  • FM stands for frequency modulation, another method of carrying information.
  • (a) A carrier wave at the station's basic frequency.